A recursive algorithm for an efficient and accurate computation of incomplete Bessel functions

In a previous work, we developed an algorithm for the computation of incomplete Bessel functions, which pose as a numerical challenge, based on the G(n)((1)) transformation and Slevinsky-Safouhi formula for differentiation. In the present contribution, we improve this existing algorithm for incomplete Bessel functions by developing a recurrence relation for the numerator sequence and the denominator sequence whose ratio forms the sequence of approximations. By finding this recurrence relation, we reduce the complexity from O(n(4)) to O(n). We plot relative error showing that the algorithm is capable of extremely high accuracy for incomplete Bessel functions.

Automated summary

This study improves the algorithm for computing incomplete Bessel functions by developing a recurrence relation and reducing the complexity. The results show extremely high accuracy.